Question

The first term of an arithmetic sequence is -3 and thefifth term is 53 what is the common difference of the sequence

Answer 1

In an arithmetic sequence, you start from the first element, and then you generate the next one by adding a common difference.

So, let's say you start from
`x` and add a common difference of
`d`. The first elements are

`a_1=x`

`a_2=x+d`

`a_3=(x+d)+d=x+2d`

`a_4=(x+2d)+d=x+3d`

`a_5=(x+3d)+d=x+4d`

Since we know that
`a_5 = 53`, and
`x = -3`, we can solve for
`d`:

`a_5 = x+4d \iff 53 = -3+4d \iff 56 = 4d \iff d = (56)/(4) = 14`

So, the common difference is 14